Don't get on the lawn upkeep treadmill, if you can help it. All the grass sold in big box stores are going to require irrigation and chemicals for weeds and all that shit. It's a bunch of bullshit pushed to keep you paying. Billion dollar industry and all that.
Order some native seed if you can. When I was researching, I think I saw a place that was near OKC, but many of them ship, so it's not like you have to pick it up local. You will need to do your own research on what kind of grow speed, maximum height, minimum mowed height, resilience to drought, and other such things for your area. You may be able to call/email one of the shops that sell native seed, and see if they can just recommend a mix.
For example, parts of Texas can grow
Buffalo grass. It has a maximum height of 5-8 inches, highly drought resistant (as little as 12in/year), and if you want it shorter, you only need to mow every one or two months in the summer (at least, according to the internet).
The best place I found, with good info (at least for Texas) is down between Austin and San Antonio:
Discover and Buy Thunder Turf at Native American Seed
www.seedsource.com
If you can find a map like this of OK, you should be able to figure what will work up there. OSU has an article with some maps that look similar, but they are too small to read:
HERE
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